Ostoja-Starzewski publishes paper extending continuum mechanics in Proceedings of the Royal Society
MechSE professor Martin Ostoja-Starzewski has had a paper published in the Royal Society journal Proceedings of the Royal Society A. As the national academy of science in the United Kingdom, the Royal Society is a fellowship of the world's most eminent scientists and is the oldest scientific academy in continuous existence.
A summary of the article and research follows:
"The entire field of continuum mechanics and physics (including all of fluid and solid mechanics) has been developed subject to the axiom of Second Law of thermodynamics, requiring a non-negative rate of irreversible entropy production. Given the results in contemporary physics, this law, however, has to be restricted to macroscales because on very small scales and (very) short times, the entropy production rate may become negative. The violations of the Second Law have been demonstrated by theory, experiments, and simulations over the past two decades. In fact, in some cases (e.g., for micron sized latex particles trapped by radiation pressure in an optical trap) the Second Law can be violated for macroscopic (!) times, namely three seconds, or so. Results of that type suggest that an extension of continuum mechanics (and physics) should be made, wherein the Second Law axiom ought to be relaxed, and this task has defined the goal of the paper just published by Prof. Martin Ostoja-Starzewski in the Proceedings of Royal Society A; download from [https://www.researchgate.net/profile/Martin_Ostoja-Starzewski].
"In effect, the evolution of entropy at every continuum point is stochastically (not deterministically) conditioned by the past history, so that the Clausius-Duhem inequality is replaced by the fluctuation theorem. With his co-author, Anatoliy Malyarenko (at Mälardalen University in Sweden), Martin Ostoja-Starzewski recognizes the entropy to evolve as a submartingale. The ensuing mathematics – via the Doob decomposition theorem – allows classification of all the thermomechanical processes into four types depending on whether they are conservative or not and/or conventional continuum mechanical or not. Incidentally, the theory of martingales was developed just across the Green St. in the Altgeld Hall by one of the great mathematicians of the 20th century: Joseph L. Doob. While his martingales, submartingales, and supermartingales have been known to describe the games of chance and, hence, gambling and financial markets … with all their splendors and miseries, they have now found an application also in theoretical mechanics of fine-scale fluids and solids.
"The just-published paper proposes modeling a wide range of continua (e.g., thermofluids with parabolic or hyperbolic heat conduction) via stochastic field models, possibly including spatial fractal and Hurst effects. As a ready illustration of violations of the Second Law, counterintuitive blow-ups of acceleration wavefronts of nanoscale thickness are studied. Of the many other important implications stemming from the entropy production becoming negative every now and then two are quite tangible for those working in mechanics: (i) nanomachines (or even mitochondria in a cell) spend part of their time actually running in "reverse"; (ii) if an extremely small jet engine were to run in "reverse", it would take in ambient heat and exhaust fumes to generate kerosene and oxygen [http://en.wikipedia.org/wiki/Fluctuation_theorem]."
Ostoja-Starzewski joined the MechSE Department and the University of Illinois at Urbana-Champaign in 2006. He holds a PhD in mechanical engineering from McGill University.
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